On the Colored Jones Polynomial, Sutured Floer homology, and Knot Floer homology

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dc.creatorGrigsby, J. Elisenda
dc.creatorWehrli, Stephan
dc.date2008-07-09
dc.date2008-10-13
dc.date.accessioned2026-07-07T10:08:58Z
dc.date.available2026-07-07T10:08:58Z
dc.descriptionLet K in S^3 be a knot, and let \widetilde{K} denote the preimage of K inside its double branched cover, Σ(K). We prove, for each integer n > 1, the existence of a spectral sequence from Khovanov's categorification of the reduced n-colored Jones polynomial of the mirror of K to the knot Floer homology of (Σ(K),\widetilde{K}) (when n odd) and to (S^3, K # K) (when n even). A corollary of our result is that Khovanov's categorification of the reduced n-colored Jones polynomial detects the unknot whenever n>1.
dc.description46 pages, 13 figures; Unnecessary assumptions in statement of link surgeries spectral sequence (Section 4) removed, references updated, minor typos corrected throughout
dc.identifierhttps://arxiv.org/abs/0807.1432
dc.identifierhttp://arxiv.org/abs/0807.1432
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/171184
dc.subjectGeometric Topology
dc.subjectQuantum Algebra
dc.subjectSymplectic Geometry
dc.subject57M27; 57R58; 57M12; 81R50
dc.titleOn the Colored Jones Polynomial, Sutured Floer homology, and Knot Floer homology
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